The Y = 1/6 Asymmetry: Why the Cabibbo Doublet Fixes the Gap Ratio. Small hypercharge, large correction.

The Y = 1/6 Asymmetry: Why the Cabibbo Doublet Fixes the Gap Ratio. Small hypercharge, large correction. This paper is part of the HOWL research archive—a collection of physics papers exploring integer fraction derivations across multiple domains using exact arithmetic and automated comparison. Abstract The Cabibbo Doublet (3,2,1/6) fixes the Standard Model gap ratio with one particle because its hypercharge Y = 1/6 is the smallest nonzero value possible for a color triplet weak doublet with standard electric charges. The beta function contribution to b₁ (the hypercharge coupling) is proportional to Y², making Δb₁ = 1/15 — tiny. The contributions to b₂ (weak coupling) and b₃ (strong coupling) are independent of Y, giving Δb₂ = 1 and Δb₃ = 1/3. The resulting asymmetry ratio Δb₂/Δb₁ = 15 is the highest of any candidate in the 15-particle enumeration. This extreme asymmetry produces a double action on the gap ratio: the numerator (b₁ − b₂) shrinks by 13% because Δb₂ overwhelms Δb₁, while the denominator (b₂ − b₃) grows by 17% because Δb₂ exceeds Δb₃. Both effects push the gap ratio from 218/115 = 1.896 down to 38/27 = 1.407, within 0.049 of the measured 1.358. Increasing Y to any other value degrades the correction monotonically — at Y = 1/2, the gap ratio distance is already 3.4 times worse. The optimum at Y = 1/6 is sharp, not broad. The scalar version of (3,2,1/6) has the same asymmetry ratio but half the magnitude, reaching only 1.632 — five times worse. The Cabibbo Doublet is not merely a survivor of the elimination cascade. It is the uniquely optimal single-multiplet correction to the SM gap ratio, and the mechanism is exact rational arithmetic on the representation quantum numbers. Falsification Criteria All papers in this archive are subject to falsification through direct comparison to published experimental measurements. Each derived value is tested against independent data with explicit PASS/FAIL criteria. Any derived value that fails its comparison is documented and published alongside the successes. Research Context This archive documents an ongoing research program in integer fraction physics. The methodology is: derive values from gauge group integers using exact fraction arithmetic, compare to published measurements, and document all results including failures. The archive spans multiple physics domains connected through the soliton boundary framework described in the constituent papers. Package Contents manuscript.md: The complete derivation and supporting analysis. README.md: Navigation, dependencies, and citation (Registry: HOWL-PHYS-18-2026). Dependencies: HOWL-PHYS-1-2026, HOWL-PHYS-10-2026, HOWL-PHYS-11-2026, HOWL-PHYS-12-2026, HOWL-PHYS-13-2026, HOWL-PHYS-14-2026, HOWL-PHYS-15-2026, HOWL-PHYS-17-2026, HOWL-PHYS-2-2026, HOWL-PHYS-6-2026, HOWL-PHYS-7-2026, HOWL-PHYS-8-2026, HOWL-PHYS-9-2026 Motto: Derive. Compare. Publish.Status: Complete